The Dutchman has been on the books at Roma since the summer of 2018, but has so far struggled to establish himself at the capital club.
Kluivert has had several stints away from Rome on loan, with the latest being at Ligue 1 side Nice last term.
The 23-year-old has one more season left on his current deal at the Stadio Olimpico, but Giallorossi coach Jose Mourinho does not see him playing a big part in his plans.
Roma are open to selling Kluivert in the ongoing window and Ligue 1 giants Marseille are keen to take him back to France.
But according to Italian daily Tuttosport, Premier League outfit West Ham also have the Dutchman in their sights and have tested the water over a possible move for him in recent days.
Hammers boss David Moyes is keen on bolstering his attacking department and Kluivert is one of the names on his radar.
West Ham are also claimed to be open to letting go of one of their own wingers in the shape of Said Benrahma in the ongoing window, with Moyes keen to bring in an upgrade for him and it remains to be seen whether they will push for Kluivert this summer.
